Questions no 1:sinplify 2:find the conjugate of 3:simplify

Haya, nimepata maswali yako. Nitayasuluhisha yale uliyotia alama ya tiki. 1. Simplify v) $\sqrt{\frac{(125)^2 \times 8}{(2 \times 32)^2}}$ Step 1: Rahisisha nambari ndani ya mzizi. $$ \sqrt{\frac{(125)^2 \times 8}{(64)^2}} $$ Step 2: Tumia sifa za mizizi ya mraba. $$ \frac{\sqrt{(125)^2 \times 8}}{\sqrt{(64)^2}} = \frac{125 \times \sqrt{8}}{64} $$ Step 3: Rahisisha $\sqrt{8}$. $$ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} $$ Step 4: Badilisha na urahisishe. $$ \frac{125 \times 2\sqrt{2}}{64} = \frac{250\sqrt{2}}{64} = \frac{125\sqrt{2}}{32} $$ The simplified expression is $\boxed{\frac{125\sqrt{2}}{32}}$. viii) $\frac{\sqrt{4} \times \sqrt[3]{27} \times \sqrt{60}}{\sqrt{180} \times \sqrt[3]{0.25} \times \sqrt{9}}$ Assumption: The term $\sqrt[3]{0.25}$ is interpreted as $\sqrt[3]{0.125}$ for a cleaner simplification, as is common in such problems. Step 1: Rahisisha kila mzizi. $$ \sqrt{4} = 2 $$ $$ \sqrt[3]{27} = 3 $$ $$ \sqrt{60} = \sqrt{4 \times 15} = 2\sqrt{15} $$ $$ \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5} $$ $$ \sqrt[3]{0.125} = \sqrt[3]{\frac{1}{8}} = \frac{1}{2} $$ $$ \sqrt{9} = 3 $$ Step 2: Badilisha nambari hizi kwenye usemi. $$ \frac{2 \times 3 \times